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Friction-induced vibration (FIV) is very common in engineering areas.Analysing the dynamic behaviour of systems containing a multiple-contact pointfrictional interface is an important topic. However, accurately simulatingnonsmooth/discontinuous dynamic behaviour due to friction is challenging. Thispaper presents a new physics-informed neural network approach for solvingnonsmooth friction-induced vibration or friction-involved vibration problems.Compared with schemes of the conventional time-stepping methodology, in thisnew computational framework, the theoretical formulations of nonsmoothmultibody dynamics are transformed and embedded in the training process of theneural network. Major findings include that the new framework not only canperform accurate simulation of nonsmooth dynamic behaviour, but also eliminatethe need for extremely small time steps typically associated with theconventional time-stepping methodology for multibody systems, thus saving muchcomputation work while maintaining high accuracy. Specifically, four kinds ofhigh-accuracy PINN-based methods are proposed: (1) single PINN; (2) dual PINN;(3) advanced single PINN; (4) advanced dual PINN. Two typical dynamics problemswith nonsmooth contact are tested: one is a 1-dimensional contact problem withstick-slip, and the other is a 2-dimensional contact problem consideringseparation-reattachment and stick-slip oscillation. Both single and dual PINNmethods show their advantages in dealing with the 1-dimensional stick-slipproblem, which outperforms conventional methods across friction models that aredifficult to simulate by the conventional time-stepping method. For the2-dimensional problem, the capability of the advanced single and advanced dualPINN on accuracy improvement is shown, and they provide good results even inthe cases when conventional methods fail.

Physics-informed neural network for friction-involved nonsmooth dynamics problems